I haven't used that script1, but it looks like it duplicates both partitions into an .img file, then tar & gzips that. To extract the .img:
tar -xzf whatever.tar.gz
You can then mount and work with the partitions in the image following the instructions here. You can also use the .img to create an SD card following these instructions.
Note that you should not copy stuff from the second partition wholesale into a running system because: A) it will fail at certain points (/proc, /sys) -- hopefully; B) it will overwrite stuff in /run, /var, etc. that will likely screw up the system in very noticeable ways.
1. Because my answer to that question makes more sense ;) Once implemented, it's faster, easier, and safer (since if you use that backup image the wrong way, you will screw up your system as explained above). I explain other reasons there why dd is NOT a good tool for the purpose of maintaining a backup. I also explain how to restore from a (proper) backup using rsync...
